Question

The position vectors of $P$ and $Q$ are respectively $a$ and $b$. If $R$ is a point on $\overrightarrow{PQ}$ such that $\overrightarrow{PR}=5\overrightarrow{PQ}$, then the position vector of $R$ is

• A. $5b-4a$
• B. $5b+4a$
• C. $4b-5a$
• D. $4b+5a$

Answer 1

The correct option is A $5b-4a$

Given, $\overrightarrow{PR}=5\overrightarrow{PQ}$

$\Rightarrow \overrightarrow{R}-\overrightarrow{P}=5(\overrightarrow{Q}-\overrightarrow{P})$

$\Rightarrow \overrightarrow{R}=5\overrightarrow{Q}-5\overrightarrow{P}+\overrightarrow{P}$

$\Rightarrow \overrightarrow{R}=5\overrightarrow{Q}-4\overrightarrow{P}$

$\Rightarrow R=5b-4a$